216
THEORY OF
SPECIFIC
HEAT
along
a
straight
line,
and
denotes
its
instantaneous
distance
from
the
equilibrium
position
and
velocity
by x
and
E, respectively,
one
obtains
-
E
(2a) dV
-
Ce
^
dxd£
,
and
since
one
has
to
take
jdxd£
=
const.dE, hence
w =
const.1:
(3a)
dW =
const.
e
dE.EN
The
mean
value of the
mass
particle's
energy
is therefore
(4) E
-
JL
F
Ee
RT
dE
RT
TT-T
e
RT
dE
It is
obvious
that formula
(4)
can
also
be
applied
to
a
rectilinearly
oscillating ion. If
one
does
so,
and
takes into
account that,
according to
a
study
by
Planck2,
the relation
[8] (5)
\
=
» K
must
hold
between
its
mean energy
E
and
the
density
pv of
the
black-body
radiation
at
the
frequency
considered there, then
by
eliminating
E
from
(4)
and
(5)
one
arrives
at Rayleigh's
formula
r_-I
(a\
n
R
8lP2
m
[9]
(6) ^
=
which,
as
is well
known,
represents
only
a
limiting
law
for
large
values
of
[10]
T/v.
1Because
one
has
to set E
=
ax2
+
b£2.
2M.
Planck,
Ann. d.
Phys.
1
(1900):
99.
[7]